Dictionaries notwithstanding, underway just looks like a mistake to my eye. It gives the appearance that the writer has got it confused with underpass and underwear.
It is a similar mistake that people make with everyday. As an adverb, every day is correct because both words carry their full weight e.g. I jog every day. But the two words are joined to form an adjective as in everyday clothes. If every and day are not joined to form a compound adjective, they should at least be joined by a hyphen: every-day clothes to show that the writer has created a new adjective. (Decline in the use of the hyphen is another subject ripe for a rant!)
There is no reason to join the adverbs under way or every day with a hyphen, so it follows that there is no need to join them together at all.